Score : $500$ points

Problem Statement

Given are $N$ distinct points in a two-dimensional plane. Point $i$ $(1 \leq i \leq N)$ has the coordinates $(x_i,y_i)$.

Let us define the distance between two points $i$ and $j$ be $\mathrm{min} (|x_i-x_j|,|y_i-y_j|)$: the smaller of the difference in the $x$-coordinates and the difference in the $y$-coordinates.

Find the maximum distance between two different points.

Constraints

• $2 \leq N \leq 200000$
• $0 \leq x_i,y_i \leq 10^9$
• $(x_i,y_i)$ $\neq$ $(x_j,y_j)$ $(i \neq j)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$x_1$ $y_1$

$x_2$ $y_2$

$\vdots$

$x_N$ $y_N$

Output

Print the maximum distance between two different points.

3
0 3
3 1
4 10

4

The distances between Points $1$ and $2$, between Points $1$ and $3$, and between Points $2$ and $3$ are $2$, $4$, and $1$, respectively, so your output should be $4$.

4
0 1
0 4
0 10
0 6

0

8
897 729
802 969
765 184
992 887
1 104
521 641
220 909
380 378

801